It is believed the flags were stolen some time over the weekend.
They had been flying above the Dunedin City Council's Great King St car park building to help people decide how to vote in the New Zealand flag referendum.
Council property unit asset manager John Varney said the theft shocked council staff as reaching the flags would have been difficult.
The flag ropes could only be accessed high up the poles and a scissor lift had been needed to put them up, Mr Varney said.
Council staff believed the thief or thieves might have backed a large vehicle up to the flagpoles and then climbed on to it to access the ropes.
They would have needed a tool with considerable reach, possibly some kind of tree pruner, to chop the flag ropes.
This suggested the theft was not a spur-of-the-moment decision.
The culprits would ''definitely'' have been visible to anyone in the street.
A New Zealand Flag Consideration Project spokeswoman said the theft was disappointing and it had offered the council a new set of flags.
Another set of the flags was stolen in Kaitaia.
Council corporate services group manager Sandy Graham said the council would not be replacing the flags.
The stolen flags had been flying for nearly six weeks and it would cost money to put new ones up.
